The invention relates to a polarization grating for diffractive light deflection, having at least one liquid-crystal layer on a substrate or between at least two substrates, the liquid-crystal molecules having a periodic variation of their orientation. The invention also relates to a light deflection device in which at least one such polarization grating is contained, and to a method for light deflection which uses at least one such polarization grating. The invention relates to both reflective and transmissive polarization gratings, in which case reflective polarization gratings may also be formed as liquid-crystal layers on a silicon substrate (LCOS, Liquid Crystal On Silicon). The invention also relates to an apparatus for the reconstruction of holographically encoded three-dimensional scenes, and to a device for directing solar radiation onto a photosensitive surface, which respectively contain at least one such polarization grating.
Diffractive light deflecting means have a wide range of use. They may for example be used for passive and active beam or wavefront shaping, or generally as diffractive optical imaging means. They can be produced wavelength- and/or angle-selectively, so that beam combination or beam splitting can be carried out with them, as is for example required in optical networks. Advantageously, they can be used for the tracking of a small observer region onto the eyes of a user in a stereoscopic or holographic display. Another field of application consists, for example, in the concentrating and/or tracking of solar radiation onto a photosensitive surface.
Polarization gratings for light deflection are diffraction gratings with a fixed or variable grating period. In diffraction gratings, at a predetermined wavelength λ of the light, the grating period Λ establishes the angle of deflection βm:
      β    m    =      arcsin    ⁡          (                                    m            ⁢                                                  ⁢            λ                    Λ                -                  sin          ⁡                      (            α            )                              )      
In this case, m is an integer which indicates the diffraction order, and α is the angle of incidence, or entry angle.
In general, diffraction gratings may have a periodic surface structure (surface relief gratings) or the optical properties may vary periodically within the layer influencing the light. The periodic optical properties may influence the amplitude and/or the phase and/or the polarization of the light.
In a diffraction grating, the strength and the profile of the optical variation determine the diffraction efficiency with which the light is deflected into the individual diffraction orders. The diffraction efficiencies are also dependent on the angle of incidence into the polarization grating, since the effective optical properties vary with the angle of incidence. For most applications, however, a high diffraction efficiency, also referred to as diffraction effectiveness, is required over a wide range of the angles of incidence.
Polarization gratings—unlike for example surface relief gratings—have the property that it is possible to obtain almost 100% diffraction efficiency in a single diffraction order. In contrast to other grating types with a high diffraction efficiency, such as volume gratings, which constitute so-called thick gratings, polarization gratings can be formed as thin gratings. The term thin grating relates to the fact that the thickness of the layer acting as a diffraction grating is less than its period. In a thick grating, the thickness of the layer acting as a diffraction grating is much greater than its period.
In comparison with other grating types which allow a high diffraction efficiency, for example volume gratings (volume Bragg gratings), which have a narrow angle of incidence range, polarization gratings can have a high diffraction efficiency for a relatively wide angle of incidence range. This angle range may for example be ±15° or even ±20°. Nevertheless, this is not sufficient for a number of applications.
Polarization gratings can be configured as passive gratings, as switchable gratings with a fixed grating period or as gratings whose grating period can be controlled.
The present invention relates primarily to switchable and controllable polarization gratings, but may also be used for passive gratings. Switchable gratings with a fixed grating period are often produced in a thin birefringent, i.e. optically anisotropic, liquid-crystal layer (LCPG—Liquid-Crystal Polarization Grating), which is located between two substrates acting as a boundary of the liquid-crystal cell. Light which does not travel in the direction of the crystal optical axis of the liquid-crystal molecules accordingly experiences a positive or negative phase retardation of the extraordinary ray relative to the ordinary ray, depending on whether the birefringence of the liquid-crystal material is positive or negative, this retardation being greatest when the light ray travels perpendicularly to the crystal optical axis. Positive birefringence in this case means that the difference between the refractive indices Δnp for the extraordinary ray ne and the ordinary ray no is greater than zero (Δnp=ne−no>0), and negative birefringence means that this difference Δnn is less than zero (Δnn=ne−no<0). By suitable alignment of the liquid-crystal molecules in the liquid-crystal layer, or relative to one another, a phase change of the two elementary rays with respect to one another, and therefore of the polarization state of the light travelling through the liquid-crystal layer, can therefore be achieved. The desired alignment of the liquid-crystal molecules may, for example, be adjusted during the production of the liquid-crystal cell. To this end, the gratings have alignment layers on one or both substrate sides, which lead to suitable alignment of the liquid-crystal molecules in the active liquid-crystal layer. In polarization gratings with a fixed grating period, the alignment layers are structured periodically in correspondence with the grating spacing, i.e. the grating period. Such alignment layers may, for example, be produced via polymerization of a photosensitive polymer by irradiation with a suitable exposure distribution, as described for example in U.S. Pat. No. 7,196,758 B2 or in International Patent Application WO 2006/092 758 A2. On the alignment layers, the liquid crystals are aligned with their crystal optical axes in such a way that a periodic variation of the polarization state of the light passing through is achieved.
The alignment layers may also be structured by shaping the alignment pattern with the aid of micro-structured templates.
Switchable LCPGs with a fixed grating period have an electrode structure which is formed on the substrates. It may be formed uniformly or structured, in order to permit position-dependent switching. By application of a suitable voltage to the electrode structure, the liquid-crystal molecule alignment imposed by the alignment layer can be removed, so that the mutual orientation thereof is lost, or the crystal optical axis comes to lie in the light propagation direction. The birefringence of the liquid-crystal layer is removed, and the polarization grating therefore becomes inactive, so that light only leaves the liquid-crystal layer undeviated, i.e. into the 0th diffraction order.
Passive polarization gratings may be produced in a similar way as switchable gratings with a fixed grating period, likewise by using liquid-crystal molecules. In this case, the liquid molecules may for example be embedded in a polymerizable monomer, which is polymerized after its alignment so that the alignment state is frozen in. In this case, it is also possible to operate only with a substrate and an alignment layer (WO 2006/092 758 A2).
Passive and switchable gratings with a fixed grating period have a fixed angle of deflection at a predetermined wavelength.
Gratings whose grating period can be controlled are described, for example, in International Application WO 2011/067 265 A1 of the same Applicant. They have a fine-structured, individually drivable electrode structure on one or more substrate sides. By applying an electric field in the plane of the liquid-crystal layer (in-plane), the rotation angle of the liquid-crystal molecules can be influenced. This may, for example, be achieved by applying a voltage to a neighboring electrode pair, which lies on one substrate side. By applying a suitable periodic voltage profile to the electrode structure, the desired alignment of the liquid-crystal molecules is achieved in the active layer, which lies between two substrates, so that adequate periodic variation of the polarization state of the incident light takes place. In this case, for a predetermined wavelength and a predetermined angle of incidence, the period of the voltage profile determines the angle of deflection. For example, the electrodes may be arranged in the form of a comb on a substrate. A voltage profile which acts in the plane of the liquid-crystal layer, and leads to a variation of the alignment of the liquid crystals in the liquid-crystal layer, may be applied to such an electrode structure. The alignment of the liquid crystals in the voltageless state is in this case likewise induced by one or more alignment layers, which in this case may also be unstructured.
With this type of gratings, the angle of deflection can be modified by varying the grating period.
Polarization gratings may operate reflectively or transmissively. A reflective polarization grating is described, for example, in U.S. Pat. No. 6,924,870 B1.
Polarization gratings with a fixed grating period may be structured with small grating periods, and therefore large angles of deflection. For polarization gratings with an adjustable grating period, the maximum resolution achievable in the structuring of the electrode structure, and the individual driving thereof, limit the maximum achievable angle of deflection.
From liquid-crystal display screens, arrangements of nematic liquid crystals which have a twist, so-called twisted nematic (TN) modes, are also known. In a TN liquid-crystal cell, the orientation of the alignment layers on the two substrates differs, for example by 90°. Owing to the elastic energy of the liquid crystals, continuous twisting over the liquid-crystal layer is then set up. Cholesteric liquid-crystal phases, which contain chiral molecules and form a helical structure of their orientation, are also known. Such a helical structure likewise has a twist. Often, therefore, TN liquid-crystal mixtures also have an admixture of chiral dopants, i.e. the doped liquid-crystal molecules do not have a rotation mirror symmetry axis. These dopants induce twisting of the liquid crystal. The twisting in the TN cell is then not only caused by the orientation on the alignment layers, but is also reinforced by the tendency of the liquid crystals to form a twisted structure anyway.
In a polarization grating with a fixed grating period, there is a periodic variation of the orientation of the alignment layers. If the alignment layers on the two sides of such a polarization grating are displaced laterally relative to one another in terms of their structuring, then the alignment can vary along the surface normal of the liquid-crystal layer, i.e. the molecules experience an additional twist along the surface normal. Over the range of one grating period, the orientation on an alignment layer varies by 350°. For example, a 90° twist from one alignment layer to the other then corresponds to a lateral displacement of the orientation of the two alignment layers with respect to one another by one fourth of a grating period.
Since chiral liquid-crystal mixtures already have a twist, such a twisted liquid-crystal layer can even be set up when only one alignment layer is provided. This makes it possible to produce polarization gratings with a fixed grating period, in which the orientation of the liquid molecules has a twist and which only require one substrate, when the liquid-crystal molecules are for example bound in a polymer matrix. The twist angle can in this case be adjusted through the composition of the material, that is through the quantitative proportion and the type of the chiral dopant.
International Patent Application WO 2008/130 555 A1 describes a polarization grating with a twist. The use of chiral dopants is likewise described therein, in order to obtain a polarization grating with a twist on a single alignment layer. Two-layer polarization gratings with different periodic alignment layers on a substrate and between the two passive liquid-crystal layers are also described. The two liquid-crystal layers have, for example, an opposite twist and have achromatic properties, i.e. they have a high diffraction efficiency at a plurality of wavelengths. However, they have a high diffraction efficiency only for a narrower angle of incidence range.
The liquid-crystal molecules may also have a tilt relative to the plane of the liquid-crystal layer. Such a tilt angle may, for example, be adjusted or controlled by an electric field transverse to the plane of the liquid-crystal layer. Such a field may be generated by applying an electric voltage to an electrode pair, each electrode being located on one of the two substrate surfaces.
Polarization gratings may be configured in such a way that the light is preferably diffracted with almost 100% efficiency into the +1st or −1st diffraction order, dependent on the polarization state of the incident light.
The diffraction efficiency n±1 for the ±1st order is calculated for a grating with a layer thickness d and the birefringence Δn of the liquid-crystal layer as:
      η          ±      1        =                    1        ⁢                  +          _                ⁢                  S          3          ′                    2        ⁢                  sin        2            ⁡              (                              πΔ            ⁢                                                  ⁢            nd                    λ                )            where S3′ is the normalized Stokes parameter S3/S0. The Stokes parameters S0−S3 describe the polarization state of the incident light.
For circularly polarized light, therefore, a diffraction efficiency n±1 of 100% is achieved when the birefringence is Δn=λ/2d. If, for example, the incident light is right-circularly polarized, then S3′=−1 and all light is diffracted into the 1st diffraction order. Regarding its thickness, such a polarization gracing corresponds to a λ/2 plate. In contrast to a λ/2 plate with a fixed optical axis, however, in the case of polarization gratings the angle of the optical axis in the grating plane varies locally. This angle rotates through 180° within one grating period. When passing through the birefringent liquid-crystal layer, the light experiences a relative phase change corresponding to a λ/2 plate, so that it is left-circularly polarized after leaving the plate. Left-circularly polarized light would, corresponding to S3′=1, be diffracted into the −1st diffraction order, and would leave the grating as right-circularly polarized light. The diffraction efficiency η0 of the 0th order is calculated as:
      η    0    =            cos      2        ⁡          (                        πΔ          ⁢                                          ⁢          nd                λ            )      
It is independent of the polarization state of the incident light. For a birefringence Δn=λ/2d, the 0th diffraction order is substantially suppressed. For a birefringence different to Δn=λ/2d, the 0th diffraction order is present. With a suitable selection of the polarization state of the incident light (circularly polarized), however, the polarization state of the 0th order differs from that of the ±1st order. If, for example, the incident light is left-circularly polarized, then the 0th order is likewise left-circularly polarized but the −1st order is right-circularly polarized, and the +1st order has an intensity close to 0. This can advantageously be used for filtering of the diffraction orders. A circular polarizer, which is arranged downstream of the polarization grating, may for example block the 0th order and transmit the −1st order.
With a given layer thickness, the diffraction efficiency is thus dependent on the wavelength and the birefringence.
An efficiency of close to 100% in the +1st or −1st diffraction order is ordinarily achieved only for normal incidence of the light. With an oblique angle, the efficiency decreases, and at the same time the undesired fraction of the undiffracted light of the 0th order usually increases.
Polarization gratings may also be produced with a plurality of layers. In this case, for example, the alignment pattern of the liquid-crystal molecules of the individual layers may differ from one another, or be displaced relative to one another. Such arrangements are for example likewise described in International Patent Application WO 2006/092 758 A2 or in International Patent Application WO 2008/130 561 A1, in order for example to obtain polarization gratings which have a high diffraction efficiency for a wide wavelength range (achromatic polarization gratings).
If the direction of incidence of the light varies, than the effective layer thickness also varies. This effect increases when the angle of incidence becomes greater. However, the effective birefringence of the liquid-crystal layer (LC layer) also varies for light which passes through the cell obliquely with respect to the orientation of the liquid-crystal molecules (LC molecules). It becomes less with oblique transit. In general, this effect dominates that of the greater geometrical layer thickness, so that the effective optical path length for oblique transit is less. If the liquid-crystal molecules are modified in their orientation by an electric field, then, in the case of a pixel with a uniform liquid-crystal orientation, this may for example lead to the effective birefringence becoming greater for light which is incident obliquely from the left and the effective birefringence becoming less for light which is obliquely incident from the right. In a conventional liquid-crystal cell for amplitude modulation, in some technologies a structure with a plurality of subregions of different liquid-crystal orientation is used in order to compensate for this effect (multidomain structure).
In a polarization grating with periodic orientation of the LC molecules, a tilt of the LC molecules out of the plane of the substrates would cause a periodically variable effective optical path length for the obliquely incident light. The grating is then no longer a pure polarization grating, but instead is additionally superimposed with components of different grating types. In general, almost 100% diffraction efficiency is therefore not achieved in an individual diffraction order.
In devices in which a plurality of focusing or light-deflecting components are used in series, however, light which has already been deflected by a preceding component sometimes strikes the subsequent elements obliquely. For example, a holographic display may contain a plurality of components in succession for focusing light and for observer tracking. Light may, for example, first be focused by a field lens and then obliquely strikes a polarization grating, the task of which is to deflect the light further.
If a plurality of controllable elements in series are used, then the angle at which the light strikes the last element may vary depending on the way in which the preceding elements are driven. These controllable elements may, for example, be a stack of polarization gratings in which the overall angle of deflection is generated by a different combination of the angles of deflection of individual gratings.
In general, the entry or incidence angle of the light into a polarization grating may, for example, be adjusted or varied by a combination of different diffractive elements, such as volume gratings, or refractive elements, such as prisms, which are arranged in the light path before the polarization grating.
Also, for example, in solar applications the angle of incidence may vary with the position of the sun.